2x(x^2+x)4x=0

Solution for 2x(x^2+x)4x=0 equation:

Simplifying
2x(x2 + x) * 4x = 0

Reorder the terms:
2x(x + x2) * 4x = 0

Reorder the terms for easier multiplication:
2 * 4x * x(x + x2) = 0

Multiply 2 * 4
8x * x(x + x2) = 0

Multiply x * x
8x2(x + x2) = 0
(x * 8x2 + x2 * 8x2) = 0
(8x3 + 8x4) = 0

Solving
8x3 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x3'.
8x3(1 + x) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-1}